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I am wondering is there any program to draw the Wigner-Seitz
cell from the coordinates of ions in a unit cell? My second potentially stupid question is: a slab is repeated in x, y, and and in z-direction with a gap of vacuum layer. How to determine how many times it is repeated in x, y- and z- direction with k-mesh 9x9x1.

Thanks

For your second question, this follows from the Born - von Karman periodic boundary conditions. In a large but finite crystal the allowed k values are

k = m1/N2*g1 + m1/N2*g2 + m3/N3*g3

where g:s are the reciprocal lattice vectors, N:s are the size of the crystal in integer multiples of the primitive translations vectors, 0<m<N are integers.

Or as a corollary to the above statement, an infinite system approximated by a finite set of k points (such as a periodic plane wave DFT calculation) corresponds to the situation of a finite system with the number of units cells equal to the number of k points (all the k-points, not only the irreducible ones). For a supercell calculation, you must multiply by the number of primitive unit cells in the supercell.

Or something like that.